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Conventional and Unconventional Monetary Policy Rate Uncertainty and Stock Market Volatility: A Forecasting Perspective

  • Ruipeng Liu EMAIL logo , Mawuli Segnon , Rangan Gupta and Elie Bouri
Published/Copyright: September 17, 2025
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Studies in Nonlinear Dynamics & Econometrics
From the journal Studies in Nonlinear Dynamics & Econometrics

Abstract

Theory suggests the existence of a bi-directional relationship between stock market volatility and monetary policy rate uncertainty. In light of this, we forecast volatilities of equity markets and shadow short rates (SSR) – a common metric of both conventional and unconventional monetary policy decisions, by applying a bivariate Markov-switching multifractal (MSM) model. Using daily data of eight advanced economies (Australia, Canada, Euro area, Japan, New Zealand, Switzerland, the UK, and the US) over the period of January 1995 to February 2025, we find that the bivariate MSM model outperforms, in a statistically significant manner, not only the benchmark historical volatility and the univariate MSM models, but also the Dynamic Conditional Correlation Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) framework, particularly at longer forecast horizons. Our findings are robust to different out-of-sample periods, and superiority of the bivariate MSM is also confirmed relative to the corresponding Generalized Autoregressive Score (GAS) model. This finding confirms the bi-directional relationship between stock market volatility and uncertainty surrounding conventional and unconventional monetary policies, which in turn has important implications for academics, investors and policymakers.

Keywords: shadow short rate uncertainty; stock market volatility; markov-switching multifractal model (MSM); forecasting
JEL Classification: C22; C32; C53; D80; E52; G15
Corresponding author: Ruipeng Liu, Deakin Business School, Deakin University, 221 Burwood Highway, Melbourne, VIC 3125, Australia, E-mail: 

We would like to thank an anonymous referee for many helpful comments. However, any remaining errors are solely ours.

Ruipeng Liu, Mawuli Segnon, Rangan Gupta, and Elie Bouri contributed equally to this work.

Appendix

Bivariate Generalized Autoregressive Score (GAS) Models

The bivariate GAS(1,1) framework proposed by Creal et al. (2013) assumes that the 2 × 1 vector of returns at time t, r t , is generated by the observational density.

(10) r t ∼ p ( r t | f t , F t − 1 ; θ ) ,

where F t − 1 denotes the sigma algebra generated by the history of the time series up to time t and f t is a vector of time-varying parameters which fully characterizes density function p(.) and only depends on F t − 1 and a set of static parameters θ . The time-varying parameters f t in Eq. 10 are driven by the scaled score function of the conditional distribution and a first order autoregressive component as:

(11) f t + 1 = ω + A s t + B f t ,

the coefficients vector or matrices ω , A, B in Eq. 11 have proper dimensions, and the scaled score function s t is given by

(12) s t = S t ∇ t ,

where

∇ t = ∂ ⁡ ln ⁡ p ( r t ; f t ) ∂ f t ,

and

S t ≔ I t f t − γ ,

with

I t f t ≔ E t − 1 ∇ t ∇ t ′ = − E t − 1 ∂ 2 ⁡ ln ⁡ p ( r t ; f t ) ∂ f t ∂ f t ′ ,

where γ takes value in the set {0, 0.5, 1}. The quantity s t in Eq. 12 updates the time-varying parameters from f t to f t+1. The updating procedure is similar to the well known Newton Raphson algorithm. In the empirical section we use the recently developed R-Package ”GAS” by Ardia et al. 2019 that is based on the estimation approach proposed in Creal et al. (2013).

Table A1:

Volatility forecasts: DCC-GARCH model (Out-of-Sample: 16/08/2008–26/02/2025).

Horizon Australia Canada EU Japan
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.808 0.623 0.821 0.608 0.886 0.788 0.859 0.523
5 0.873 0.966 0.879 0.779 0.913 0.945 0.916 0.963
10 0.918 0.999 0.936 0.843 0.944 0.994 0.940 1.134
20 0.968 1.001 0.975 0.914 0.975 0.997 0.980 1.235
50 0.994 1.002 0.997 1.151 0.990 0.996 1.000 1.491
100 0.997 1.003 1.000 2.263 0.992 0.996 1.007 1.558
RMAE
1 0.946 0.766 0.951 0.360 1.022 0.815 0.876 0.530
5 0.959 0.983 0.975 0.460 1.031 0.996 0.908 0.859
10 0.977 1.012 1.007 0.526 1.046 1.012 0.935 1.083
20 1.002 1.015 1.035 0.633 1.060 1.013 0.972 1.324
50 1.025 1.017 1.062 0.988 1.076 1.014 1.015 1.581
100 1.029 1.018 1.071 1.655 1.083 1.015 1.028 1.635
New Zealand Switzerland UK USA
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.839 0.976 0.891 0.471 0.885 0.631 0.842 0.900
5 0.906 1.492 0.932 0.882 0.926 0.983 0.897 0.978
10 0.952 1.971 0.967 0.974 0.964 0.993 0.945 0.995
20 0.988 3.285 0.994 0.994 0.989 0.999 0.981 1.002
50 1.002 4.761 1.007 0.995 0.995 0.999 0.998 1.003
100 1.004 5.322 1.012 0.996 0.996 0.999 1.001 1.004
RMAE
1 0.955 0.603 0.994 0.634 1.012 0.705 0.984 0.761
5 0.980 1.325 1.030 1.019 1.029 0.978 1.017 0.984
10 0.995 2.032 1.057 1.076 1.047 1.005 1.050 1.030
20 1.016 3.333 1.079 1.087 1.062 1.013 1.080 1.046
50 1.029 4.138 1.095 1.088 1.076 1.014 1.108 1.048
100 1.031 5.579 1.102 1.094 1.082 1.014 1.118 1.049

  1. This table reports the multi-horizon volatility forecast performances based on the DCC-GARCH(1,1) model for the shadow short rate (SSR) returns of 8 countries/regions: Australia, Canada, Eurozone, Japan, New Zealand, Switzerland, the UK, and the US and their corresponding MSCI index returns. We report the relative MSE (RMSE) and relative MAE (RMAE) measurements, computed by dividing the MSE and MAE estimates by the pertinent MSE and MAE of the naive volatility predictor (using historical volatility), therefore any values smaller than 1 indicate an improvement against historical volatility.

Table A2:

Volatility forecasts: Univariate multifractal model (Out-of-Sample: 16/08/2008–26/02/2025).

Horizon Australia Canada EU Japan
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.909 0.780 0.902 0.562 0.922 0.819 0.885 0.606
5 0.944 0.920 0.949 0.679 0.950 0.948 0.942 0.859
10 0.960 0.951 0.968 0.696 0.966 0.959 0.956 0.903
20 0.975 0.963 0.983 0.709 0.979 0.966 0.973 0.916
50 0.985 0.973 0.995 0.714 0.991 0.982 0.981 0.917
100 0.994 0.985 0.999 0.721 0.997 0.994 0.985 0.939
RMAE
1 0.947 0.782 0.885 0.363 0.970 0.871 0.821 0.536
5 0.962 0.833 0.894 0.466 0.964 0.979 0.849 0.682
10 0.967 0.860 0.909 0.489 0.969 0.990 0.863 0.733
20 0.982 0.889 0.923 0.536 0.975 0.992 0.882 0.776
50 1.003 0.940 0.941 0.630 0.977 1.000 0.911 0.818
100 1.020 0.985 0.955 0.726 0.982 1.001 0.935 0.867
New Zealand Switzerland UK USA
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.884 0.738 0.894 0.709 0.926 0.859 0.890 0.862
5 0.923 0.887 0.939 0.913 0.956 0.960 0.939 0.964
10 0.941 0.911 0.950 0.954 0.969 0.972 0.962 0.978
20 0.963 0.937 0.972 0.980 0.982 0.981 0.982 0.982
50 0.982 0.963 0.986 0.994 0.991 0.991 0.998 0.992
100 0.996 0.969 0.995 0.996 0.996 0.997 1.001 0.994
RMAE
1 0.943 0.560 0.893 0.750 0.950 0.797 0.878 0.767
5 0.951 0.709 0.908 0.934 0.952 0.935 0.890 0.876
10 0.956 0.747 0.921 0.959 0.960 0.953 0.906 0.894
20 0.970 0.793 0.939 0.971 0.969 0.966 0.922 0.914
50 0.990 0.876 0.969 0.975 0.977 0.984 0.940 0.955
100 1.006 0.925 0.996 0.979 0.988 1.000 0.951 0.982

  1. This table reports the multi-horizon volatility forecast performances based on the univariate multifractal model for the shadow short rate (SSR) returns of 8 countries/regions: Australia, Canada, Eurozone, Japan, New Zealand, Switzerland, the UK, and the US and their corresponding MSCI index returns. We report the relative MSE (RMSE) and relative MAE (RMAE) measurements, computed by dividing the MSE and MAE estimates by the pertinent MSE and MAE of the naive volatility predictor (using historical volatility), therefore any values smaller than 1 indicate an improvement against historical volatility.

Table A3:

Volatility forecasts: DCC-GARCH model (Out-of-Sample: 01/01/2020–26/02/2025).

Horizon Australia Canada EU Japan
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.819 0.804 0.836 0.882 0.938 0.900 0.922 0.603
5 0.891 1.003 0.924 1.202 0.962 0.918 0.983 1.061
10 0.953 1.127 0.979 1.334 0.983 0.973 0.999 1.066
20 0.992 1.137 0.998 1.386 0.995 0.990 1.002 1.065
50 1.000 1.184 1.000 1.761 0.999 0.993 1.009 1.078
100 0.989 1.183 1.027 3.704 1.006 0.993 1.012 1.080
RMAE
1 0.899 0.833 0.898 0.748 0.973 0.876 0.935 0.600
5 0.916 0.973 0.939 0.959 0.992 0.998 0.957 0.940
10 0.941 1.056 0.978 1.088 1.013 1.024 0.981 1.078
20 0.967 1.089 1.004 1.263 1.030 1.029 0.996 1.180
50 0.977 1.242 1.021 1.926 1.038 1.031 1.011 1.223
100 0.971 1.329 1.035 3.154 1.051 1.031 1.014 1.227
New Zealand Switzerland UK USA
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.938 0.555 0.954 0.436 0.918 0.727 0.808 0.959
5 0.956 1.255 0.968 0.860 0.949 1.081 0.905 1.092
10 0.984 1.707 0.994 0.979 0.977 1.010 0.964 1.059
20 0.995 2.280 1.005 0.998 0.995 0.997 0.993 1.006
50 0.999 4.940 1.007 0.998 0.999 0.999 0.997 1.000
100 1.001 5.135 1.071 0.998 1.014 0.999 1.029 1.003
RMAE
1 0.997 0.767 0.989 0.673 0.949 0.829 0.961 0.883
5 1.003 1.300 1.025 0.969 0.980 1.048 1.006 1.112
10 1.004 1.653 1.063 1.008 1.005 1.038 1.038 1.143
20 1.006 2.364 1.086 1.014 1.027 1.012 1.063 1.143
50 1.006 3.704 1.098 1.014 1.040 1.018 1.076 1.169
100 1.008 5.076 1.119 1.020 1.056 1.017 1.117 1.186

  1. This table reports the multi-horizon volatility forecast performances based on the DCC-GARCH(1,1) model for the shadow short rate (SSR) returns of 8 countries/regions: Australia, Canada, Eurozone, Japan, New Zealand, Switzerland, the UK, and the US and their corresponding MSCI index returns. We report the relative MSE (RMSE) and relative MAE (RMAE) measurements, computed by dividing the MSE and MAE estimates by the pertinent MSE and MAE of the naive volatility predictor (using historical volatility), therefore any values smaller than 1 indicate an improvement against historical volatility.

Table A4:

Volatility forecasts: Univariate multifractal model (Out-of-Sample: 01/01/2020–26/02/2025).

Horizon Australia Canada EU Japan
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.849 0.741 0.884 0.813 0.953 0.822 0.926 0.722
5 0.897 0.994 0.937 0.986 0.971 0.910 0.951 0.959
10 0.940 1.009 0.970 1.044 0.972 0.966 0.964 1.009
20 1.006 1.018 0.988 1.038 0.979 0.976 0.985 1.062
50 1.013 1.088 0.998 1.007 0.998 0.985 0.994 1.062
100 1.032 1.118 1.027 1.023 0.998 0.987 1.003 1.018
RMAE
1 0.914 0.859 0.837 0.703 0.958 0.979 0.897 0.585
5 0.936 1.043 0.864 0.823 0.971 1.101 0.916 0.730
10 0.953 1.123 0.887 0.856 0.991 1.141 0.928 0.782
20 0.994 1.158 0.922 0.855 1.017 1.156 0.936 0.836
50 1.035 1.270 0.971 0.861 1.030 1.213 0.952 0.848
100 1.104 1.226 0.970 0.857 1.047 1.306 0.945 0.856
New Zealand Switzerland UK USA
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.945 0.586 0.944 0.656 0.926 0.896 0.837 0.911
5 0.957 0.826 0.961 0.819 0.953 0.984 0.897 0.959
10 0.984 0.926 0.980 0.898 0.964 0.988 0.931 0.972
20 0.992 1.033 1.015 0.913 1.002 0.978 1.002 0.987
50 0.998 1.165 1.026 0.949 1.023 0.993 1.016 0.999
100 1.001 1.064 1.027 0.969 1.013 0.989 1.024 0.992
RMAE
1 1.022 0.824 0.876 0.825 0.916 0.882 0.923 0.884
5 1.021 1.013 0.895 0.977 0.933 1.009 0.946 0.990
10 1.025 1.083 0.908 1.040 0.945 1.053 0.972 1.028
20 1.038 1.177 0.929 1.107 0.966 1.059 1.014 1.027
50 1.046 1.305 0.932 1.067 1.002 1.110 1.057 1.115
100 1.076 1.177 0.962 1.080 1.024 1.126 1.083 1.128

  1. This table reports the multi-horizon volatility forecast performances based on the univariate multifractal model for the shadow short rate (SSR) returns of 8 countries/regions: Australia, Canada, Eurozone, Japan, New Zealand, Switzerland, the UK, and the US and their corresponding MSCI index returns. We report the relative MSE (RMSE) and relative MAE (RMAE) measurements, computed by dividing the MSE and MAE estimates by the pertinent MSE and MAE of the naive volatility predictor (using historical volatility), therefore any values smaller than 1 indicate an improvement against historical volatility.

Table A5:

Volatility forecasts: univariate GAS model (Out-of-Sample: 16/08/2008–26/02/2025).

Horizon Australia Canada EU Japan
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.810 0.726 0.706 1.115 0.835 0.517 0.861 1.487
5 0.914 0.942 0.899 1.139 0.978 0.993 1.001 1.636
10 0.958 0.978 1.005 1.037 0.995 1.013 1.004 1.109
20 0.997 1.004 1.043 1.006 1.005 1.018 1.008 1.022
50 1.005 1.025 1.013 1.017 1.003 1.018 1.007 1.023
100 1.011 1.028 1.004 1.030 1.005 1.018 1.005 1.021
RMAE
1 0.939 0.963 0.926 0.995 0.977 1.227 0.961 7.440
5 0.962 0.996 0.950 1.042 1.004 0.990 0.988 1.197
10 0.964 0.986 0.965 1.004 1.002 0.998 0.984 0.965
20 0.969 0.981 0.968 0.946 0.999 1.001 0.975 0.958
50 0.963 0.983 0.951 0.920 0.975 1.001 0.955 0.956
100 0.960 0.983 0.942 0.920 0.965 1.000 0.943 0.954
New Zealand Switzerland UK USA
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.865 192.561 0.825 1.776 0.827 1.281 0.799 0.884
5 0.968 1.009 0.977 1.002 0.953 0.989 0.922 0.992
10 0.986 1.021 1.001 1.008 0.981 1.002 0.963 1.005
20 0.997 1.022 1.010 1.008 1.000 1.004 0.999 1.008
50 1.005 1.022 1.004 1.008 1.001 1.004 1.005 1.008
100 1.017 1.023 0.990 1.015 0.999 1.004 0.998 1.008
RMAE
1 0.968 3.594 0.923 49.453 0.961 0.898 0.902 29.444
5 0.991 0.969 0.950 0.982 0.990 0.982 0.933 0.982
10 0.984 0.972 0.954 0.987 0.989 0.992 0.941 0.992
20 0.976 0.972 0.952 0.987 0.985 0.996 0.949 0.996
50 0.966 0.971 0.948 0.986 0.963 0.996 0.953 0.996
100 0.959 0.968 0.952 0.985 0.956 0.995 0.955 0.995

  1. This table reports the multi-horizon volatility forecast performances based on the univariate GAS model for the shadow short rate (SSR) returns of 8 countries/regions: Australia, Canada, Eurozone, Japan, New Zealand, Switzerland, the UK, and the US and their corresponding MSCI index returns. We report the relative MSE (RMSE) and relative MAE (RMAE) measurements, computed by dividing the MSE and MAE estimates by the pertinent MSE and MAE of the naive volatility predictor (using historical volatility), therefore any values smaller than 1 indicate an improvement against historical volatility.

Table A6:

Volatility forecasts: univariate GAS model (Out-of-Sample: 01/01/2020–26/02/2025).

Horizon Australia Canada EU Japan
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.810 0.726 0.706 1.115 0.835 0.517 0.861 1.487
5 0.914 0.942 0.899 1.139 0.978 0.993 1.001 1.636
10 0.958 0.978 1.005 1.037 0.995 1.013 1.004 1.109
20 0.997 1.004 1.043 1.006 1.005 1.018 1.008 1.022
50 1.005 1.025 1.013 1.017 1.003 1.018 1.007 1.023
100 1.011 1.028 1.004 1.030 1.005 1.018 1.005 1.021
RMAE
1 0.963 0.933 0.952 1.040 0.992 0.786 0.991 1.319
5 0.987 1.006 0.991 1.088 1.017 0.988 1.017 1.626
10 0.991 1.000 1.035 1.046 1.021 1.001 1.006 0.983
20 0.999 0.994 1.042 0.996 1.013 1.006 0.993 0.952
50 0.980 1.006 0.998 0.992 0.984 1.005 0.971 0.945
100 0.958 1.006 0.943 0.999 0.964 1.004 0.955 0.940
New Zealand Switzerland UK USA
MSCI SSR MSCI SSR MSCI SSR MSCI SSR
RMSE
1 0.865 1.561 0.825 1.776 0.827 1.281 0.799 0.884
5 0.968 1.009 0.977 1.002 0.953 0.989 0.922 0.992
10 0.986 1.021 1.001 1.008 0.981 1.002 0.963 1.005
20 0.997 1.022 1.010 1.008 1.000 1.004 0.999 1.008
50 1.005 1.022 1.004 1.008 1.001 1.004 1.005 1.008
100 1.017 1.023 0.990 1.015 0.999 1.004 0.998 1.008
RMAE
1 1.009 3.802 0.951 3.430 0.971 0.964 0.918 0.836
5 1.035 1.004 0.973 0.986 0.999 0.991 0.962 0.985
10 1.023 1.012 0.985 0.992 1.000 1.004 0.972 1.003
20 1.006 1.014 0.980 0.992 0.995 1.009 0.983 1.011
50 0.986 1.014 0.965 0.990 0.972 1.010 0.979 1.013
100 0.974 1.012 0.957 0.982 0.950 1.007 0.959 1.009

  1. This table reports the multi-horizon volatility forecast performances based on the univariate GAS model for the shadow short rate (SSR) returns of 8 countries/regions: Australia, Canada, Eurozone, Japan, New Zealand, Switzerland, the UK, and the US and their corresponding MSCI index returns. We report the relative MSE (RMSE) and relative MAE (RMAE) measurements, computed by dividing the MSE and MAE estimates by the pertinent MSE and MAE of the naive volatility predictor (using historical volatility), therefore any values smaller than 1 indicate an improvement against historical volatility.

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Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/snde-2024-0108).

Received: 2024-10-01
Accepted: 2025-08-28
Published Online: 2025-09-17

© 2025 Walter de Gruyter GmbH, Berlin/Boston

https://doi.org/10.1515/snde-2024-0108
Keywords for this article
shadow short rate uncertainty; stock market volatility; markov-switching multifractal model (MSM); forecasting
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